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euler-011.clj
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(in-ns 'project-euler)
(clojure.core/use 'clojure.core)
(def twenty-twenty-grid [
[ 8 2 22 97 38 15 0 40 0 75 4 5 7 78 52 12 50 77 91 8]
[49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 4 56 62 0]
[81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 3 49 13 36 65]
[52 70 95 23 4 60 11 42 69 24 68 56 1 32 56 71 37 2 36 91]
[22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80]
[24 47 32 60 99 3 45 2 44 75 33 53 78 36 84 20 35 17 12 50]
[32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70]
[67 26 20 68 2 62 12 20 95 63 94 39 63 8 40 91 66 49 94 21]
[24 55 58 5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72]
[21 36 23 9 75 0 76 44 20 45 35 14 0 61 33 97 34 31 33 95]
[78 17 53 28 22 75 31 67 15 94 3 80 4 62 16 14 9 53 56 92]
[16 39 5 42 96 35 31 47 55 58 88 24 0 17 54 24 36 29 85 57]
[86 56 0 48 35 71 89 7 5 44 44 37 44 60 21 58 51 54 17 58]
[19 80 81 68 5 94 47 69 28 73 92 13 86 52 17 77 4 89 55 40]
[ 4 52 8 83 97 35 99 16 7 97 57 32 16 26 26 79 33 27 98 66]
[88 36 68 87 57 62 20 72 3 46 33 67 46 55 12 32 63 93 53 69]
[ 4 42 16 73 38 25 39 11 24 94 72 18 8 46 29 32 40 62 76 36]
[20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 4 36 16]
[20 73 35 29 78 31 90 1 74 31 49 71 48 86 81 16 23 57 5 54]
[ 1 70 54 71 83 51 54 69 16 92 33 48 61 43 52 1 89 19 67 48]])
(defn new-x-y
"Get new x & y based on direction and a single increment"
[pos-x pos-y direction]
(let [new-pos-y
(cond
(= direction :left) (- pos-y 1)
(= direction :right) (+ pos-y 1)
(= direction :diag-up-left) (- pos-y 1)
(= direction :diag-up-right) (+ pos-y 1)
(= direction :diag-down-left) (- pos-y 1)
(= direction :diag-down-right) (+ pos-y 1)
true pos-y)
new-pos-x
(cond
(= direction :up) (- pos-x 1)
(= direction :down) (+ pos-x 1)
(= direction :diag-up-left) (- pos-x 1)
(= direction :diag-up-right) (- pos-x 1)
(= direction :diag-down-left) (+ pos-x 1)
(= direction :diag-down-right) (+ pos-x 1)
true pos-x)]
[new-pos-x new-pos-y]))
(defn product-in-direction
"Find the product of n consecutive numbers
in any direction for a given position in an nxn vector."
[grid pos-orig-x pos-orig-y direction number]
(let [max-x (count grid) max-y (count (grid 0)) min-x 0 min-y 0]
(loop [pos-x pos-orig-x pos-y pos-orig-y count-number number product 1]
(if (= count-number 0)
product
(let [
new-pos-x-y (new-x-y pos-x pos-y direction) new-count-number (- count-number 1)
new-product
(* product
(if (or (>= pos-x max-x) (< pos-x min-x) (>= pos-y max-y) (< pos-y min-y))
1
((grid pos-x) pos-y)))]
(recur (new-pos-x-y 0) (new-pos-x-y 1) new-count-number new-product))))))
(defn max-product-in-any-direction
"Find the maximum product in any direction for any position in an nxn vector"
[grid pos-x pos-y number]
(max
(product-in-direction grid pos-x pos-y :left number)
(product-in-direction grid pos-x pos-y :right number)
(product-in-direction grid pos-x pos-y :up number)
(product-in-direction grid pos-x pos-y :down number)
(product-in-direction grid pos-x pos-y :diag-up-left number)
(product-in-direction grid pos-x pos-y :diag-up-right number)
(product-in-direction grid pos-x pos-y :diag-down-left number)
(product-in-direction grid pos-x pos-y :diag-down-right number)))
(loop [pos-x 0 pos-y 0 product 1 max-x 0 max-y 0]
(if (and (>= pos-x 20) (>= pos-y 20))
product
(let [current-product (max-product-in-any-direction twenty-twenty-grid pos-x pos-y 4)]
(recur
(if (= pos-y 20) (+ pos-x 1) pos-x)
(if (= pos-y 20) 0 (+ pos-y 1))
(if (> current-product product) current-product product)
(if (> current-product product) pos-x max-x)
(if (> current-product product) pos-y max-y)))))